Problem: Rewrite as a simplified fraction. ${0.38\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 382.2222...\\ 100x &= 38.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 344}$ ${x = \dfrac{344}{900}} $ ${x = \dfrac{86}{225}} $